65.24 GeneratorMat

GeneratorMat( C )

GeneratorMat returns a generator matrix of C. The code consists of all linear combinations of the rows of this matrix.

If until now no generator matrix of C was determined, it is computed from either the parity check matrix, the generator polynomial, the check polynomial or the elements (if possible), whichever is available.

If C is a non-linear code, the function returns an error.

    gap> GeneratorMat( HammingCode( 3, GF(2) ) );
    [ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
      [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ],
      [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ],
      [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ] ]
    gap> GeneratorMat( RepetitionCode( 5, GF(25) ) );
    [ [ Z(5)^0, Z(5)^0, Z(5)^0, Z(5)^0, Z(5)^0 ] ]
    gap> GeneratorMat( NullCode( 14, GF(4) ) );
    [  ]
    gap> GeneratorMat( ElementsCode( [[0, 0, 1 ], [1, 1, 0 ]], GF(2) ));
    Error, non-linear codes don't have a generator matrix 

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